Question

The refractive index of the material of a prism is $\sqrt{2}$ and its angle is $30^{\circ} .$ One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is

• A. $60^{\circ}$
• B. $0^{\circ}$
• C. $30^{\circ}$
• D. $45^{\circ}$

Answer 1

Answer: (D)

If the ray retraces its path, means the light ray hits the mirrored surface normally.
$\Rightarrow r_{2}=0$
$A=r_{1}+r_{2}$
$\Rightarrow 30^{\circ}=r_{1}+0$
$\frac{\sin i}{\sin r_{1}}=\mu$ or $\frac{\sin i}{\sin 30^{\circ}}=\sqrt{2}$
$\Rightarrow \sin i=\frac{1}{\sqrt{2}}$ or $i=45^{\circ}$